Existing Multimodal Large Language Models (MLLMs) struggle with 3D spatial reasoning, as they fail to construct structured abstractions of the 3D environment depicted in video inputs. To bridge this gap, drawing inspiration from cognitive theories of allocentric spatial reasoning, we investigate how to enable MLLMs to model and reason over text-based spatial representations of video. Specifically, we introduce Textual Representation of Allocentric Context from Egocentric Video (TRACE), a prompting method that induces MLLMs to generate text-based representations of 3D environments as intermediate reasoning traces for more accurate spatial question answering. TRACE encodes meta-context, camera trajectories, and detailed object entities to support structured spatial reasoning over egocentric videos. Extensive experiments on VSI-Bench and OST-Bench demonstrate that TRACE yields notable and consistent improvements over prior prompting strategies across a diverse range of MLLM backbones, spanning different parameter scales and training schemas. We further present ablation studies to validate our design choices, along with detailed analyses that probe the bottlenecks of 3D spatial reasoning in MLLMs.

3D visual grounding (3DVG) is challenging due to the need to understand 3D spatial relations. While supervised approaches have achieved superior performance, they are constrained by the scarcity and high annotation costs of 3D vision-language datasets. Training-free approaches based on LLMs/VLMs eliminate the need for large-scale training data, but they either incur prohibitive grounding time and token costs or have unsatisfactory accuracy. To address the challenges, we introduce a novel method for training-free 3D visual grounding, namely **La**nguage-to-**S**pace **P**rogramming (LaSP). LaSP introduces LLM-generated codes to analyze 3D spatial relations among objects, along with a pipeline that evaluates and optimizes the codes automatically. Experimental results demonstrate that LaSP achieves 52.9% accuracy on the Nr3D benchmark, ranking among the best training-free methods. Moreover, it substantially reduces the grounding time and token costs, offering a balanced trade-off between performance and efficiency.